The ratio of SI Unit to CGS unit of Planck's constant is

Options

A. `10^7`
B. `10^(-7)`
C. `10^3`
D. `10^5`

Answer

To find the ratio of the SI unit to the CGS unit of Planck's constant, we will follow these steps:

### Step 1: Identify the SI unit of Planck's constant
The SI unit of Planck's constant (H) is given as:
\[ \text{SI unit of } H = \text{kg} \cdot \text{m}^2/\text{s} \]

### Step 2: Identify the CGS unit of Planck's constant
The CGS unit of Planck's constant is given as:
\[ \text{CGS unit of } H = \text{g} \cdot \text{cm}^2/\text{s} \]

### Step 3: Convert the SI unit to CGS unit
We need to convert the SI unit (kg, m, s) into CGS units (g, cm, s).

1. **Convert kilograms to grams**:
\[ 1 \text{ kg} = 10^3 \text{ g} \]

2. **Convert meters to centimeters**:
\[ 1 \text{ m} = 10^2 \text{ cm} \]

### Step 4: Substitute the conversions into the SI unit
Now, substituting these conversions into the SI unit of Planck's constant:
\[ \text{SI unit of } H = (10^3 \text{ g}) \cdot (10^2 \text{ cm})^2/\text{s} \]
\[ = (10^3 \text{ g}) \cdot (10^4 \text{ cm}^2)/\text{s} \]
\[ = 10^{3 + 4} \text{ g} \cdot \text{cm}^2/\text{s} \]
\[ = 10^7 \text{ g} \cdot \text{cm}^2/\text{s} \]

### Step 5: Calculate the ratio of SI unit to CGS unit
Now we can find the ratio of the SI unit to the CGS unit:
\[ \text{Ratio} = \frac{\text{SI unit}}{\text{CGS unit}} = \frac{10^7 \text{ g} \cdot \text{cm}^2/\text{s}}{1 \text{ g} \cdot \text{cm}^2/\text{s}} \]
\[ = 10^7 \]

### Conclusion
The ratio of the SI unit to the CGS unit of Planck's constant is:
\[ \text{Ratio} = 10^7 \]

The correct option is **10 raised to 7**.

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